In a two-stage ko taking the ko produces another ko mouth, which must be taken before winning the ko. Example:
See Nidan Ko Examples.
Having an unfavorable two stage ko is better than have an unfavorable approach ko, because if the first ko is won in an approach ko, the player will next have to fight a normal ko, but if the first ko is won in a two stage ko, the player will be fighting a favorable two stage ko.
-- Andre Engels
Two step ko Two stage ko Discussion